Algebra

Question 1

Simplifying expressions

Answer 1

Combine like terms by adding coefficients. Ex. 3xy + 2x -xy - 3x = 2xy - x

Question 2

Multiplying polynomials using FOIL (First, Outer, Inner, Last)

Answer 2

(a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2; (a^2 - b^2) = (a + b)(a - b)

Question 3

Factoring using Greatest Common Factors

Answer 3

A # or variable that is a factor of each term in an algebraic expression can be factored out. Ex. 4x + 12 = 4(x + 3); 15y^2 - 9y = 3y(5y - 3)

Question 4

Factoring using difference of squares

Answer 4

(a + b)(a - b) = (a^2 - b^2) ; Ex. (2x + 5)(2x - 5) = 4x^2 - 25 ; 4x^2 - 9y^2 = (2x + 3y)(2x - 3y)

Question 5

Factoring using quadratic polynomials

Answer 5

x^2 + ax + b = (x + m)(x + n), where a is the sum of m and n, and b is their product

Question 6

Factoring rational expressions

Answer 6

Ex. (x^2 - 9)/(4x - 12) = (x + 3)(x - 3)/4(x - 3) = (x + 3)/4

Question 7

Golden rule of solving equations

Answer 7

“What you do to one side of an equation, you must also do to the other.”

Question 8

Eliminating fractions

Answer 8

(a/b)(b/a) = 1 Ex. (2/5)x = 8 -> (5/2)(2/5)x = (5/2)8 -> x = 20

Question 9

Solve: Multiply by the LCD

Answer 9

(3x/4) + (1/2) = (x/3), multiply by 12, (36x/4) + (12/2) = (12x/3) -> 9x + 6 = 4x, x = -(6/5)

Question 10

Cross-multiplication

Answer 10

(a/b) = (c/d) -> ad = bc

Question 11

Quadratic equations

Answer 11

ax^2 + bx + c, where a is not 0; if you can factor it to (x + a)(x - b) = 0, then the solutions are -a and b

Question 12

Quadratic formula

Answer 12

If ax^2 + bx + c = 0, and a is not 0, then x = (-b ± √(b^2 - 4ac))/2a

Question 13

Two variables/systems of equations (Substitution)

Answer 13

One equation is manipulated to express one variable in terms of the other. Then the expression is substituted in the other equation, then solve for that variable.

Question 14

Two variables/systems of equations (Elimination)

Answer 14

Make the coefficients of one variable the same in both equations so that one variable can be eliminated either by + or - the equations.

Question 15

Function notation

Answer 15

If given f(x) = … and asked what f(something else) is, simply replace every instance of x in the “…” expression with whatever is now in the ( ). Similarly, if given a “strange operator” like xΔy and asked what aΔ2x is, just replace “x” and “y” with “a” and “2x.”

Question 16

Inequalities

Answer 16

Can be treated like regular equations, except multiplying oividing an inequality by a negative number reverses the sign of the inequality.

Question 17

Inequalities General Rules

Answer 17

If w < x & x < y, then w < y; If a < b and c < d, then a + c < b + d (doesn’t hold for subtracting, multiplying, dividing); If |x| < 3, then -3 < x < 3; if |x| > 3, then x > 3 or x < -3.

Question 18

Inequalities (quadratic)

Answer 18

If given a quadratic inequality (i.e ax^2 + bx + c < 0), first solve for when the expression is equal to 0, then use a number line to check which values of x fulfill the inequality.